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Surface tension play a crucial role in multiphase flow dynamics and more particularly in the complex interaction between liquid gas and solid. The wettability of the solid surface change deeply the dynamic of the liquid gas mixture at the three phase interface where the balance of forces gives rise to motion by capillarity. Even at high-speed flow the boundary layer may still depend on the capillarity/wettability. It is observed in coating applications targeted in the proposed work. The representative benchmark is the drag-out problem and the industrial challenge application targeted in this work is related to the steel industry and more particularly the wiping process in which a high speed air jet aimed to control the liquid film thickness.
The starting point of the PhD is a well-developed software based on anisotropic mesh adaptation and a monolithic framework for liquid gas solid dynamics (including fluid structure interaction with surface tension).

Anisotropic mesh adaptation is the only way to tackle this problem in which the size scale variations are extremes (1 meter to 1 micron-meter). The solver is based on stabilized finite element method and the mesh is dynamically adapted following a metric based a posteriori error estimate for Navier-Stokes. The mesh adaptation is fully automatic already and the PhD candidate will benefit to a high-level expertise of the team in this field.

The purpose of the PhD work is first to validate and consolidate the numerical modeling framework, to improve and to complete the time marching scheme coupled with the a posteriori anisotropic estimate and remeshing procedure. The novelty will concern the multiphase modelling and more particularly the treatment of the dynamic capillarity at the air liquid solid contact zone in a general way in high Reynolds flow contexts.

The starting based software is already used by the industrial partner of this project, providing a tightened interaction between theoretical and software developments and applications. The software based on a general library is written in C++ and can be run in 2D and in 3D on serial or parallel platform under the MPI library on Windows and Linux. It is already installed on different high-performance clusters and support a distant launching and interactive mechanism.

The data and testcases will be provide by our industrial partner able also to provide experimental data coming from online measurements which serve to compare the simulation results.

T. Coupez Metric construction by length distribution tensor and edge based error for anisotropic adaptive meshing Journal of Computational Physics 230, 7 (2011) Pages 2391-2405
T. Coupez, E. Hachem. (2013). 'Solution of high-Reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing', Computer Methods in Applied Mechanics and Engineering, 267: 65-85.
H. Digonnet, T. Coupez, P. Laure, L Silva (2019). Massively parallel anisotropic mesh adaptation. The International Journal of High Performance Computing Applications, 33(1), 3-24.

Working conditions
The proposed work will be carried out in the CFL research group Computing & Fluids located at the CEMEF Research Center of MINES ParisTech in Sophia-Antipolis, France.
This grant covers a three-year doctoral contract (including benefits) that should start in October 2022.

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